In [1]}, [2]} it was shown that \({{\mathcal {I}}}^{\Lambda ,\tau }_{G}\) 
has a remarkable property. That is, each entry \({{\mathcal {I}}}^{\Lambda ,\tau }_{G}(w,u)\) 
can be expressed in terms of a topological construction called tree of self-avoiding walks and a set influences on this tree.
The influences are specified by the parameters of our problem.
At this point, it is worth giving a high level (hence imprecise) description of the aforementioned relation.
For for further details see Section .
